29.30.2 problem 860

Internal problem ID [5442]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 860
Date solved : Monday, January 27, 2025 at 11:24:03 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

\begin{align*} x {y^{\prime }}^{2}+\left (-y+a \right ) y^{\prime }+b&=0 \end{align*}

✓ Solution by Maple

Time used: 0.092 (sec). Leaf size: 42

dsolve(x*diff(y(x),x)^2+(a-y(x))*diff(y(x),x)+b = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= a -2 \sqrt {b x} \\ y \left (x \right ) &= a +2 \sqrt {b x} \\ y \left (x \right ) &= \frac {c_{1}^{2} x +c_{1} a +b}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 58

DSolve[x (D[y[x],x])^2+(a-y[x])D[y[x],x]+b==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to a+\frac {b}{c_1}+c_1 x \\ y(x)\to \text {Indeterminate} \\ y(x)\to a-2 \sqrt {b} \sqrt {x} \\ y(x)\to a+2 \sqrt {b} \sqrt {x} \\ \end{align*}